HIV vaccines may help the immune systems of HIV infected patients better control the virus. The goal of this study is to determine whether patients on anti-HIV medications can stop taking those medications if they receive an HIV vaccine. While taking anti-HIV medications, participants will receive either an HIV vaccine or a placebo. Participants will then stop taking their anti-HIV medications and the study will compare the viral loads of participants who received the vaccine with the viral loads of participants who received the placebo.